Computer graphics processor and method for rendering a three-dimensional image on a display screen

ABSTRACT

A computer graphics processor ( 20,50 ) and a method for rendering a three-dimensional image on a display screen. The computer graphics processor ( 20,50 ) comprises a rasterizer ( 23,53 ) configured to perform pixel traversal of a primitive after projection of the primitive. Furthermore, the rasterizer ( 23,53 ) is configured to perform the pixel traversal of a first primitive for a plurality of views prior to performing pixel traversal of a next primitive for one or several views.

TECHNICAL FIELD OF THE INVENTION

The present invention relates to the field of computer graphics. Moreparticularly, the invention relates to a computer graphics processor anda method for rendering a three-dimensional image on a display screen.

DESCRIPTION OF RELATED ART

It is becoming more and more popular to provide three-dimensional (3D)images on display screens. A three-dimensional impression can e.g. becreated by using stereo images, holographic techniques, or multipleplanes in the displays, etc. Thus, a three-dimensional image may be aset of two-dimensional images created from a three-dimensional scene.That is, the set of two-dimensional images are created for generating athree-dimensional impression. The set contains at least one image.

There are different ways to produce stereo images. The images may, forexample, be time-multiplexed on a two-dimensional (2D) display, but ingeneral this requires that the viewer wear an attribute such as specialglasses. If the stereo images are displayed at the same time, the imagescan be directed to the appropriate eye by using e.g. polarized glassesor a head-mounted display. A disadvantage with this solution may be thatthe two images in general produce only a limited “look around”capability. Moreover, glasses or a head-mounted display must be worn bythe viewer to produce any 3D effect. This may be unpleasant for theviewer.

In an alternative solution, the stereo images may be split at thedisplay screen by means of a splitting screen such as a parallaxbarrier. The view of the display screen may be autostereoscopic, whichmeans that no special glasses or other peripheral equipment are requiredto view a 3D image on the display screen. However, in general thissolution works only for one viewer at a fixed position. Furthermore, the“viewing zone” may be narrow. Outside the “viewing zone”, the viewer maysee multiple images or a stereo inversion. This may in turn lead to anunpleasant view of the displayed 3D image.

A computer graphics processor (CGP) has been proposed by Emmet Kilgariffand Randy Fernando in “The GeForce Series GPU Architecture” (GPU Gems 2)edited by Matt Pharr and published by Addison Wesley in 2005. FIG. 1illustrates a block diagram of such a conventional CGP 10. The CGP 10may comprise a programmable vertex shader PVS 11. The PVS 11 may beadapted to perform per-vertex computations. The per-vertex computationsmay be applied to each vertex sent through the CGP pipeline shown inFIG. 1. The per-vertex computations may e.g. involve various matrixtransforms (in order to, for example, animate or position and orient anobject), projection, lighting computations, skinning, animation, andother per-vertex computations. In general, when the PVS 11 has finishedits operations, a vertex has been transformed into a screen space.Furthermore, various other per-vertex data, e.g., texture coordinates,attributes like diffuse and specular color may be sent downwards the CGPpipeline of FIG. 1 with the vertex. Vertices may then be grouped intoso-called primitives, such as triangles, polygons, lines, points, curvedsurfaces, etc.

Furthermore, the CGP 10 may comprise a rasterizer setup unit RSU 12. TheRSU 12 may e.g. be adapted to perform per-primitive operations, removeprimitives that are not visible, clip primitives that intersect thevisible region of the screen, or perform edge and plane equation setupon the data in preparation for rasterization, etc.

Moreover, the CGP 10 may comprise a rasterizer 13. The rasterizer 13 maybe adapted to determine which pixel locations (or samples, ifmultisampling is enabled) are covered by each projected primitive. Ingeneral, these pixel locations are called “fragments” because they canbe thought of as “candidate pixels”. This is because they may end up ina color buffer or in other buffers, e.g., a depth buffer comprised in aframe buffer 19. The fragments may be forwarded to a Z-cull unit 14. Byusing a conservative test, the Z-cull unit 14 can determine whether agroup of fragments are hidden with respect to the contents of the depthbuffer (i.e., already rendered primitives). Hence, depth reads and insome cases, also texturing and fragment program execution can be avoidedfor hidden fragments. This may increase performance.

For fragments inside the primitives that pass the Z-cull unit 14, afragment shader program may be executed in a fragment-processing unitFPU 15. The FPU 15 may e.g. be adapted to perform per-pixel computationsand memory fetches. The processing performed by the FPU 15 may beapplied to all fragments that reach the FPU 15. The FPU may e.g. beadapted to perform memory fetches from textures and merge the resultfrom the texture with other computed values, such as, realistic lightingcomputed by per-pixel diffuse and specular shading, or bump mapping,etc. The goal of the FPU 15 may be to determine the color of eachfragment.

Memory fetches performed by the FPU 15 may include access to imagetextures, and this is in general done via a texture cache memory deviceTCM 16. This may be done in order to reduce the demands on texturebandwidth. If the data is not available in the texture cache memorydevice 16, some part of the data in the cache may be removed andreplaced with the desired data that can, for example, be fetched from anexternal memory device EXM 17. The goal of the texture cache 16 is ingeneral to reduce the memory fetches from the external memory 17.

In the conventional CGP 10 shown in FIG. 1, fragments leave the fragmentprocessing unit in the order they are rasterized and sent to the“Z-compare & blend”-unit ZC&B 18. The ZC&B unit 18 may be adapted toperform, for each fragment, a depth test (comparison) against the depthbuffer e.g. for making sure that the object closest to the viewer isshown when all primitives have been rendered. The ZC&B unit 18 may alsobe adapted to perform other tests such as stencil operations, alphablending, etc. Finally, the resulting color may be written to the framebuffer 19. The frame buffer 19 may e.g. comprise a color buffer, thedepth buffer, a stencil buffer, etc. When all primitives have been sentthrough the entire CGP pipeline 10, an image has been rendered and istherefore ready to be displayed on, e.g., a display screen.

It is becoming more and more popular with multi-view systems. Multi-viewsystems can provide stereo images to several viewers at the same time,and they can be used over a relatively large viewing angle. The highernumber of views, the better image quality can in general be expected.The number of views (N) that a display is capable to show may determinethe image quality and the overall motion parallax that can berepresented on the display screen.

However, the CGP pipeline shown in FIG. 1 is used for one view only.Consequently, when the conventional CGP 10 is to be used for therendering of N multiple views, the same scene must be rendered N times,one for each view, and one at a time. In general all primitives of acertain view are processed by the entire CGP 10 before all primitives ofthe next view are processed by the entire CGP 10. This may be adisadvantage from a performance perspective. For example, when a 3Dscene is rendered, many different texture images are normally used indifferent parts of the scene. Assume that two textures, denoted T1 andT2, are used in a scene. First, T1 is applied to a set of primitives andrendered for view 1, and then T2 is applied to another set of primitivesand rendered for view 1. Since textures are in general large, and sincetexture cache memory devices are in general small, only pixels from T2will reside in the texture cache memory device 16, when the scene fromview 1 has finished rendering. However, when view 2 starts rendering,primitives with texture T1 will be rendered, and it will thus not beable to use the cache contents (which now comprise pixels from textureT2).

Furthermore, since texture data is generally fetched from the texturecache memory device 16 independently for each view, the conventional CGPmay also be expensive in terms of memory bandwidth. Alternatively, theCGP could be duplicated such that N CGPs are used in parallel. This may,however, be expensive in terms of hardware because of duplication. Inaddition, this may be costly in terms of resources. Moreover, this mayrequire synchronization between the N different CGPs.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide an improved computergraphics processor.

According to a first aspect, a computer graphics processor for renderinga three-dimensional image on a display is provided. The computergraphics processor comprises a rasterizer configured to perform pixeltraversal of a primitive after projection of the primitive. Furthermore,the rasterizer is configured to perform the pixel traversal of a firstprimitive for a plurality of views prior to performing pixel traversalof a next primitive for one or more views.

The rasterizer may be configured to perform the pixel traversal of thefirst primitive for all views of the plurality of views prior toperforming pixel traversal of the next primitive for all views of theplurality of views.

Furthermore, the rasterizer may be configured to perform pixel traversalfor a pair of the first primitive, wherein the pair is defined by agroup of pixels and a particular view, and then continue with anotherpair for the first primitive, and so on, until the first primitive hasbeen fully traversed, prior to performing pixel traversal of the nextprimitive in the same manner as for the first primitive.

Moreover, the rasterizer may be operatively connected to a selectoradapted to determine an order in which the pairs are to be processed bythe rasterizer during the pixel traversal of the primitives. Theselector may be configured to determine said order based on anefficiency measure for each view of the plurality of views. Furthermore,the selector may be configured to determine said efficiency measurebased on

$M_{i} = \left\lbrack \begin{matrix}{du} & {{\left. {dv} \right\rbrack\begin{bmatrix}{tui} \\{tvi}\end{bmatrix}},}\end{matrix} \right.$which corresponds to projecting the texture coordinate (tui,tvi) of arepresentative point of a group of pixels onto the texture traversaldirection (du,dv) in texture space, and M_(i) is the efficiency measurefor a view i, and where said group of pixels is next subject totraversal for view i, and the view that is selected for traversal nextis the view k, where M_(k) has the lowest value.

The computer graphics processor may be adapted to, for at least a firstview, generate fragments of the at least first view by executing afragment shader program. The computer graphics processor may further beadapted to, for at least a second view, generate fragments of the atleast second view based on the generated fragments of the at least firstview.

The computer graphics processor may comprise a memory and be adapted totemporarily store the generated fragments of the first view in thememory. A position of a fragment of the second view may be projectedinto the first view. If fragments of the first view in a neighborhood ofthe projected position of the fragment of the second view are stored inthe memory, the fragment of the second view may be generated based onsaid fragments in said neighborhood. Otherwise, the fragment of thesecond view may be generated by executing the fragment shader program.

The computer graphics processor may be adapted to generate texturecoordinates for the fragment of the second view and use these texturecoordinates to project the position of the fragment of the second viewinto the first view.

The computer graphics processor may be adapted to generate the fragmentof the second view based on said fragments in said neighborhood as aweighted average of said fragments in said neighborhood.

If at least two fragments of the first view in said neighborhood isstored in the memory, the fragment of the second view may be generatedby performing linear interpolation on the two of said at least twofragments that are closest to said projected position. If exactly onefragment of the first view in said neighborhood is stored in the memory,the fragment of the second view may be generated identical to saidexactly one fragment.

Two positions, whose arithmetic average is the position of the fragmentof the second view, may be projected into the first view. If fragmentsof the first view in neighborhoods of the projected positions are storedin the memory, the fragment of the second view may be generated based onsaid fragments in said neighborhoods. Otherwise, the fragment of thesecond view may be generated by executing the fragment shader program.

The computer graphics processor may be adapted to weight fragments someor all views into a common color buffer.

According to a second aspect, a method of rendering a three-dimensionalimage on a display comprising performing pixel traversal of a primitiveafter projection of the primitive is provided. The method comprises thestep of performing the pixel traversal of a first primitive for aplurality of views prior to performing pixel traversal of a nextprimitive for one or more views.

The step of performing the pixel traversal of the first primitive forthe plurality of views prior to performing pixel traversal of the nextprimitive for one or more views may comprise performing the pixeltraversal of the first primitive for all views of the plurality of viewsprior to performing pixel traversal of a next primitive for all views ofthe plurality of views.

Furthermore, the step of performing may comprise performing pixeltraversal for a pair of the first primitive, the pair being defined by agroup of pixels and a particular view, and continuing with another pairfor the first primitive, and so on, until the first primitive has beenfully traversed, prior to performing pixel traversal of the nextprimitive in the same manner as the first primitive.

The method may also comprise determining an order in which the pairs areto be processed during the pixel traversal of the primitives. The stepof determining may further comprise the steps of determining said orderbased on an efficiency measure for each view of the plurality of views,and determining said efficiency measure based on

$M_{i} = \left\lbrack \begin{matrix}{du} & {{\left. {dv} \right\rbrack\begin{bmatrix}{tui} \\{tvi}\end{bmatrix}},}\end{matrix} \right.$where Mi is the efficiency measure for a view i, and where (du, dv)denotes texture traversal direction in a texture space, (fu, fv) denotescoordinates of a pixel on the texture traversal direction in the texturespace, and (tui, tvi) denotes coordinates in the texture space for thenext pixel of view i to be subject to the traversal.

The method may comprise generating fragments of a first view byexecuting a fragment shader program and generating fragments of a secondview based on the generated fragments of the first view.

According to a third aspect, a computer program product is provided. Thecomputer program product comprises computer program code means forexecuting the method according the second aspect, when said computerprogram code means are run by an electronic device having computercapabilities.

According to a fourth aspect, a computer readable medium is provided.The computer readable medium has stored thereon a computer programproduct comprising computer program code means for executing the methodaccording to the second aspect, when said computer program code meansare run by an electronic device having computer capabilities.

Further embodiments of the invention are defined in the dependentclaims.

Embodiments of the invention may allow for a reduction of the requiredutilization of memory-bandwidth of a computer graphics processor.Furthermore, some embodiments of the invention may reduce the number offragment shader program executions of a computer graphics processor.

It should be emphasized that the term “comprises/comprising” when usedin this specification is taken to specify the presence of statedfeatures, integers, steps, or components, but does not preclude thepresence or addition of one or more other features, integers, steps,components, or groups thereof.

BRIEF DESCRIPTION OF THE DRAWINGS

Further objects, features and advantages of the invention will appearfrom the following detailed description of embodiments, reference beingmade to the accompanying drawings, in which:

FIG. 1 is a block diagram of a conventional computer graphics processor;

FIG. 2 is a block diagram of a computer graphics processor according toembodiments of the present invention;

FIG. 3 a is a pixel diagram showing a primitive projected to a screenfrom two different views;

FIG. 3 b is a screen diagram showing pixels in a texture space along atexture traversal direction for the primitive of FIG. 3 a;

FIG. 4 is a screen diagram showing tiles of pixels in the texture spacealong a texture traversal direction for a primitive; and

FIG. 5 is a block diagram of a computer graphics processor according toembodiments of the present invention.

DETAILED DESCRIPTION OF EMBODIMENTS

FIG. 2 illustrates a computer graphics processor (CGP) 20 according toembodiments of the invention. The CGP 20 may be used for rendering ofthree-dimensional images on one or more display screens. The CGP 20comprises a rasterizer 23 configured to perform pixel traversal of aprimitive after projection of the primitive. Said primitive may be atriangle, a polygon, a line, a point, a curved surface, etc. In amulti-view system with N views, the projected primitive may occupy apart of the screen space for each of the multiple N views. Furthermore,pixel traversal is the process performed by the rasterizer 23, wherebyit is determined which pixel locations (or samples, if multisampling isenabled) are inside the primitive being rendered.

The rasterizer 23 may be configured to perform the pixel traversal of afirst primitive for a plurality of views prior to performing pixeltraversal of a next primitive for one or more views. Furthermore, therasterizer 23 may be configured to perform the pixel traversal of thefirst primitive for all views of the N views prior to performing pixeltraversal of the next primitive for all views of the N views. Yetfurther, the rasterizer 23 may be configured to perform pixel traversalfor a “pair”, and then continuing with another pair, and so on, untilthe first primitive has been rendered for all or a plurality of views,prior to performing pixel traversal (in the same manner as for the firstprimitive) of a next primitive. As used herein, the term “pair” shouldbe appreciated to be defined as a group of pixels and a particular view.

In order to exemplify the above, assume that a primitive P is projectedto the different views in the display screen. The views may beenumerated from 1 to N, where N is the total number of views. Theprimitives projected to each view are called Pi, where i is the viewnumber. The projected primitive P is thus denoted P1 for the first view,P2 for the second view and PN for the Nth view, etc. According to someembodiments of the invention, a pixel traversal method may beimplemented, wherein P1 is rendered first, then P2, P3, and so on untilPN has been rendered. When a first primitive P has been rendered for allN views, a second primitive P′ for all N views may be processedsimilarly and so on for further primitives. This may allow foradvantages in terms of exploiting the coherency in rendering for Nnearby views. There is a lot of coherency herein, since the images thatare generated for, e.g., two views that are close to each other arequite similar. Therefore, when rendering a primitive that applies afragment program to each visited fragment, it is very likely that pixelsfrom textures used when rendering P1 will reside in the texture cachememory device 26 when rendering P2, P3, and so on. This is a consequenceof the fact that the images from the N different views are in generalsimilar. This may allow for an efficient utilization of the texturememory bandwidth. Accordingly, a performance advantage can be expected.This is so, since texturing is in general one of the major memorybandwidth consumers in a computer graphics processor.

Embodiments of the invention, wherein primitives are rendered for twodifferent views will be described in the following. However, this shouldnot be interpreted restrictively, but rather as an example. Thus, thereasoning below applies also for a multi-view system with N views, whereN>2. In this example, the two different views are denoted V1 and V2. Asis illustrated in FIG. 2, the CGP 20 may comprise a programmable vertexshader PVS 21 adapted to perform per-vertex computations for the twoviews V1 and V2. Some computations that depend on view parameters mayneed to be duplicated. However, there are many computations that may bethe same for both views, and these need only be computed once. Suchcomputations may include, for example, per vertex displacement mappingor diffuse shading. The PVS 21 may be operatively connected to arasterizer setup unit RSU 22.

The RSU 22 may e.g. be adapted to perform per-primitive operations,remove primitives that are not visible, clip primitives that intersectthe visible region of the screen, or perform edge and plane equationsetup on the data in preparation for rasterization, etc. The RSU 22 mayneed to duplicate some of the computations. For the two views V1 and V2,this can e.g. be done in parallel for good performance or serially tosave hardware. However, there are also computations that may be sharedbetween the two views. Such computations may include, for example, thedepth at the vertices depending on projection. The RSU 22 may be adaptedto perform setup computations for a certain primitive for both views V1and V2.

The RSU 22 may be operatively connected to a rasterizer 23. Therasterizer 23 may be adapted to locate pixels within the certainprimitive, which has been projected for both views V1 and V2, e.g. tothe screen space. In some embodiments, the rasterizer 23 may beoperatively connected to a selector 30. Although the rasterizer 23 andthe selector 30 are shown as separate units in FIG. 2, it should beappreciated that the selector 30 may alternatively be incorporated intothe rasterizer 23. The selector 30 may be adapted to determine in whichorder the rasterizer 23 should process a primitive for the views V1 andV2. Assume, for example, that V1 is selected by the selector 30 to beprocessed first. Once V1 has been selected by the selector 30, therasterizer 23 may attempt to find a pixel or a group of pixels insidethe certain primitive for view V1. Thus, the rasterizer 23 may beadapted to locate a pixel or a group of pixels inside the primitive forthe selected view. In some embodiments, the selector 30 may be adaptedto determine the above-mentioned order based on an efficiency measurefor each view of the two views V1 and V2. This will be described infurther detail hereinbelow. In general, one can say that the selector isadapted to select a pair, comprising a group of pixels and a particularview, to be processed next by the rasterizer 23. Thus, it is possible toselect a group of pixels for a view (e.g. view V2), and then continue toselect a group of pixels for another view (e.g. view V1), etc.

In some embodiments, the selector 30 may also be adapted to update theefficiency measure. Hence, when it is possible to begin processing a newpixel or group of pixels, the selector 30 may update the efficiencymeasure. Then, the selector 30 may select, in dependence of the updatedmeasure, which view of the two views to continue processing. Thisinformation may be sent to the rasterizer 23. When a view has beenselected, the rasterizer 23 may find a pixel or a group of pixels in theprimitive for that view. Thus, first some part of the primitive from thefirst view V1 may be processed by the rasterizer 23, and then some partof the primitive from the another view (possibly the same) may beprocessed by the rasterizer 23, and so on. Thus, the selector may beadapted to determine in which order the rasterizer 23 should processdifferent groups of pixels for the views V1 and V2. The selectionperformed by the selector will be described in further detailhereinbelow.

The selector 30 may also be adapted to select a pair, the pair beingdefined as a particular view and a group of pixels therein, and thenselect another pair. To exemplify this, assume that a primitive in theform of a triangle is drawn for two views V1, V2. Furthermore, assumethat the triangle comprises two groups of pixels, P1 and Q1, for viewV1. For view V2, assume that the triangle comprises two groups ofpixels, P2 and Q2. For example, Q1 and Q2 may comprise exactly the samepixels. The selector may be adapted to perform an arbitrary order forP1, P2, Q1, and Q2. Since P1 relates to view V1, one can look at P1 as apair (consisting of the group of pixels and the view). Similarly, sinceQ1 relates to view V1, one can look at Q1 as a pair (consisting of thegroup of pixels and the view). The same applies for pixel groups P2 andQ2 in view V2.

Furthermore, it should be appreciated that the selector 30 may beadapted to select a view first and then a group of pixels.Alternatively, the selector 30 may be adapted to select a group ofpixels first an then a view.

The located pixel or group of pixels may be forwarded through the CGP 20substantially similarly as for a single view in a conventional computergraphics processor. Z-cull may be performed in the Z-cull unit 24. Thismay be followed by fragment processing in a fragment-processing unit 25.The fragment-processing unit 25 may be adapted to access textures via atexture cache memory device 26. The texture cache memory device 26 maybe adapted to fetch information from an external memory device 27.Hidden surface removal and blending may then be performed for theparticular located pixel or group of pixels in an ZC&B-unit 28.Duplicated frame buffers 29 may be utilized to hold the information forboth V1 and V2.

The selection performed by the selector 30 may be accomplished indifferent ways. In an embodiment, the selector 30 is adapted todetermine an efficiency measure M based on how efficient it is tocontinue the processing with a certain view i. Each view i of the Nviews has its own efficiency measure M_(i), where i is an integer in theset {1, 2, . . . , N−1, N}. For example, the efficiency measure M_(i)may be lower the better it is to continue processing view i. Thus, whenit is time to continue processing a new pixel or a new group of pixels,processing may continue for view k, where M_(k) is the lowest of theefficiency measures M₁, M₂, . . . , M_(N).

When a pixel or group of pixels have been processed for a view k, theefficiency measure M_(k) may be updated. The efficiency measureaccording to this embodiment may e.g. be based on texture cachecontents, access patterns of different buffers, execution of fragmentshaders, or any combination thereof.

In an embodiment, the selector 30 is adapted to determine an efficiencymeasure M according to the following description. Only horizontalparallax is considered herein, i.e. only the x-coordinate differsbetween the views. This should, however, not be interpretedrestrictively, but rather as an example. In this embodiment the contentof the texture cache memory device 26 is exploited for all N views atthe same time. During the pixel traversal, rational basis functions thatrepresent normalized perspectively-correct interpolation parameters(tu,tv) may be computed for each pixel. According to McCool et al.(“Incremental and Hierarchical Hilbert Order Edge Equation PolygonRasterization” by Michael McCool, Chris Wales, and Kevin Moule, inGraphics Hardware 2001) the (tu,tv)-coordinates can be computed for eachpixel using the edge equations for a triangle. For other primitives,other methods may be employed. For a triangle there are three edgefunctions, denoted E0(x,y), E1(x,y), E2(x,y), where (x,y) is the pixelcoordinates. For a particular pixel, the coordinates (tu,tv) are thencomputed as:tu=E1(x,y)/(E0(x,y)+E1(x,y)+E2(x,y))tv=E2(x,y)/(E0(x,y)+E1(x,y)+E2(x,y))Assume that each vertex has a scalar, si, where i=0, 1, 2, and that wewant to interpolate this scalar value over the triangle with perspectivetaken into account. This is then done as:s(x,y)=(1−tu−tv)s0+tu*s1+tv*s2.It should be pointed out that other definitions and/or computations oftexture coordinates apply to our algorithm as well.

For simple notation, the normalized perspectively-correct interpolationparameters (tu,tv) may be referred to as “texture coordinates”, andthese texture coordinates may e.g. be in the range 0.0 to 1.0. Thecoordinate system where (tu,tv) resides is referred to as “texturespace”. The texture coordinates may be used to interpolate any arbitraryattributes in perspective over the primitive. For each view of the Nviews and for each point inside the primitive, there exists suchcoordinates. For view V1, the coordinates are referred to as (tu1, tv1)and for view V2, they are denoted (tu2, tv2), etc.

In FIG. 3, the background to an efficiency measure taking into accountthe texture cache memory device 26 is illustrated. A projected primitiveis shown in screen space for both view V1 101 and for view V2 102. Onlya stereo system is shown for simplicity, but it should be appreciatedthat the reasoning applies to any number of views N. A single horizontalscanline at a time is considered. The pixels in the projected primitivethat appear on the horizontal scanline are indicated in FIG. 3 a. Forview V1, these pixels are 101 a, 101 b, . . . 101 m, and for view V2,these pixels are 102 a, 102 b, . . . 102 j. In FIG. 3 b, thecorresponding pixels along the traversal direction in a texture spaceare shown for view V1 in 201, view V2 in 202, and a combination of viewsV1 and V2 in 203. The pixels of view V1 are indicated with filled ovalsand the pixels of V2 are indicated with vertical lines in FIGS. 3 a andb. Coordinate axes u and v are indicated in the combined view 203. Ascan be seen, the evenly spaced sample points in screen space areunevenly distributed in texture space due to perspective. However, theyare distributed on a straight line 250, which will be referred to as the“texture traversal direction”. Furthermore, the two views V1 and V2 mayshare this texture traversal direction due to the type of projectionthat is used. In this example, this is a consequence of that onlyhorizontal parallax is considered. This is always the case for a systemwith only two views, but for systems with more views, it is in generalrequired that all viewpoints of the views lie on a line. A horizontalscanline together with the viewpoint is equivalent to a 3D plane in theworld space, and these planes are in general identical for all theviews, and the intersection between that plane and the primitive willtherefore be the same for all views. For a planar primitive (e.g., atriangle), the intersection between the plane and the triangle will be aline (same for all views), and this line projects into a line (thetexture traversal direction) in texture space. For other primitives, theintersection will also be the same for all views, but the curve ofintersection may not be a line.

With respect to the texture cache memory device 26, an appropriate orderin which to traverse the pixels can be found by examining the screenspace samples from both views V1 and V2 in texture space, e.g. in thecombined view 203. For example, good texture cache performance may beobtained by performing the pixel traversal along the texture traversaldirection in the order in which the samples occur along the texturetraversal direction. The reason for this is, inter alfa, as follows.When a texture map is accessed, one usually wants filtered color values,using for example, trilinear mipmapping (see Lance Williams, “PyramidalParametrics”, Computer Graphics (Proceedings of ACM SIGGRAPH 83), 1983).This means that to produce a filtered color from the texture map, theneighborhood around the texture coordinates are accessed, and the colorsof these accessed pixels are weighted together to form the filteredcolor. When a filtered color has been computed, the cache contains allthe pixels from the texture that was accessed to produce the filteredcolor. Now, if the algorithm selects the closest point along the texturetraversal direction, there is generally a good chance that it ispossible to reuse the contents of the cache, compared to a case where apoint that lies farther away along the texture traversal direction ischosen. It has been shown in simulations that this is true. Let [du dv]denote a vector along the texture traversal direction. An efficiencymeasure, M_(i), for each view i can be defined by the followingexpression:

$\begin{matrix}{M_{i} = \left\lbrack \begin{matrix}{du} & {\left. {dv} \right\rbrack\begin{bmatrix}{{tui} - {fu}} \\{{tvi} - {fv}}\end{bmatrix}}\end{matrix} \right.} & (1)\end{matrix}$

where (fu,fv) is a texture coordinate on the texture traversaldirection, e.g., the texture coordinate of the first pixel on thescanline. Thus, M_(i) is simply the projection of the texture coordinateof the next pixel to be processed onto the texture traversal direction.The next view to traverse is simply the view, i, with the lowestefficiency measure, M_(i). In this way, a traversal order may beobtained that corresponds to the order of the screen space samples fromall N views in texture space. When a pixel has been visited for a view,i, the texture coordinate, (tui,tvi), for the next pixel is determined,and the efficiency measure, M_(i), can be updated. The next view totraverse to is selected as before, until all pixels (or samples) on thetexture traversal direction for all views have been visited. Then, asubsequent horizontal scanline and its corresponding texture traversaldirection is processed and so on, until pixel traversal for the entireprimitive has been performed e.g. for all views.

It should be appreciated that M_(i) is a scalar value that may be usedfor selecting an order of the pixels (or samples) to be processed, andthus M_(i) can be computed in many different ways. For example, theefficiency measure M_(i) for each view i can also be defined by thefollowing expression

$\begin{matrix}{M_{i} = \left\lbrack \begin{matrix}{du} & {\left. {dv} \right\rbrack\begin{bmatrix}{tui} \\{tvi}\end{bmatrix}}\end{matrix} \right.} & (2)\end{matrix}$This expression differs from the above expression (1) in that (fu, fv)are not included. However, the expression (2) yields the same sortedorder, since (fu,fv) may be constant for the entire scanline, and henceremoving (fu,fv) only subtracts a constant from M_(i), and thus, thesorted order may be equal. Moreover, it is also possible to find thelargest component (in absolute value) for the texture traversaldirection, and determine the sorted order based on which of the tui ortvi that corresponds to said largest component. This may give the samesorted order as well.

Hereinbelow, an example of pseudo code intended to cause a system havinga processing capability to perform a method of performing pixeltraversal according to embodiments of the invention is illustrated. Itis to be noted that only a single scanline is considered here, sinceeach scanline is processed similarly. Furthermore, it is to beappreciated that the pseudo code below only illustrates an example. Itshould be apparent that many different implementations are possible.

TraverseScanline(scanlinecoord y) * determine coordinate, xi, for theleftmost pixel inside primitive for each view on scanline y * determineli=num of pixels on current scanline for all views i * determine(tui,tvi) for all views i for leftmost pixel (xi,y) * determine(du,dv) * determine M_(i)=Equation 1 for all views i * while (pixelsleft on scanline for at least one view) * find view, j, where M_(j) isthe smallest and lj>0 * visit pixel (xj,y) using (tuj,tvj) for view j *xj = xj + 1, lj = lj − 1 * update (tuj,tvj) and M_(j) * end

An embodiment of a tiled-based pixel traversal method is presentedbelow. As used herein, a tile may be a rectangular set of pixels or anyother shape of a set of pixels. The scanline-based traversal methoddescribed above may be extended to work on a per tile basis as well.This is done by considering the pixels in FIGS. 3 a and 3 b to be tilesrather than pixels. A rectangular tile in screen space projects, ingeneral, to a convex quadrilateral in texture space. Assume that aprimitive has been rasterized. In FIG. 4, a particular row of tilescovering that primitive are shown projected into texture space for viewV1 301 and view V2 302. The projected tiles for view V1 are labeled A₁,B₁, C₁, D₁, and E₁. The projected tiles for view V2 are labeled A₂, B₂,C₂, and D₂. The projected tiles overlap the same area in texture spacefor the two views. Hence, a high texture cache performance may beobtained. This is especially true if the tiles are traversed in theorder in which they appear along the texture traversal direction. Inpractice, this amounts to differences compared with previously describedembodiments where only one pixel is considered at a time. First, thetexture coordinate, (tui, tvi), in each tile is computed, such as thecoordinate in the center of each tile. Using the coordinate in thecenter of each tile is only an example, other coordinates in the tilemay be used as well. The texture traversal direction vector, [du dv], isa vector obtained as the difference between the texture coordinates inthe center of two adjacent tiles on a row of tiles. It should beappreciated that [du dv] may be determined in a variety of ways, andthat determining the texture coordinate at the center of the tile isalso one of many possible choices. Furthermore, the traversal method isdesigned such that all tiles overlapping a primitive on a row of tilesare visited before moving on to the next row of tiles. Other choices arepossible in this regard as well. For example, the tiles may be traversedin a zigzag order. That is, instead of always traversing in a left toright order, and moving downwards to the next row of tiles, when thecurrent row of tiles has been finished, it is possible to visit thetiles in zigzag order. In zigzag order, when the end of a row of tilesis reached, one moves to the next row of tiles, and continues in theopposite (horizontal order). This gives a zigzag-like traversal order.More details about zigzag-like traversal order can be found in “Graphicsfor the Masses: A Hardware Rasterization Architecture for MobilePhones”, ACM Transactions on Graphics, July 2003, by TomasAkenine-Möller and Jacob Ström.

Shared color buffer functionality may also be provided. The shared colorbuffer may be used to accumulate fragment output values from some or allviews, and can be used to simulate, for example, depth-of field,motion-blur and anti-aliasing.

For the embodiments described above, it is to be appreciated that imagesgenerated for the N different views correspond to the images that wouldbe generated by a conventional computer graphics processor of FIG. 1when duplicated N times, or used N times (once for each view). Thus,compared to a computer graphics processor 10 as shown in FIG. 1, theperformance improvement of embodiments of the invention do not involveany degradation of the image quality.

According to other embodiments, which will be described below, a furtherperformance improvement may be obtained by approximating fragments ofsome views based on fragments generated for other views. Thereby, thenumber of fragment shader program executions may be reduced. Theadditional performance improvement comes to the cost of a slightlydegraded image quality.

FIG. 5 shows a block diagram of a CGP 50 according to an embodiment. Thecomputer graphics processor 50 may comprises a PVS 51, an RSU 52, arasterizer 53, a Z-cull unit 54, an FPU 55, a texture cache memorydevice 56, an external memory device 57, a ZC&B-unit 58, a frame buffer59, and a selector 60. These units may be configured to operatesimilarly to the corresponding elements shown in FIG. 2. In addition,the CGP 50 of FIG. 5 comprises an approximation unit 61 and a shaderoutput cache 62. Together, the approximation unit 61 and the shaderoutput cache 62 facilitates substantial reuse of the output from the FPU55.

The approximation unit 61 may be configured to classify views. Two typesof views are used: “exact” and “approximated”. Each approximated view isassociated with an exact view.

The approximation unit 61 may be configured to operate in two differentmodes depending on whether the current view is classified as “exact” or“approximated”.

For an exact view, the FPU 55 is used to execute the fragment shaderprogram, and the output of the fragment shader program, e.g. color,depth, stencil, etc., may be written to the shader output cache 62memory before being passed further down the graphics pipeline.

For an approximated view, information gathered while processing aprimitive in the exact view associated with the approximated view may beused to approximate the output that would have been obtained from thefragment shader program if the fragment shader program would haveprocessed the approximated view. A fragment coordinate of a primitive inthe approximated view is mapped (projected) onto the viewing plane ofthe associated exact view. If results of the exact view from thefragment shader program in the neighborhood of the fragment coordinatesis still in the shader output cache 62, the fragment shader programoutput for the approximated view is approximated by filtering thefragment shader program output for the exact view of the entries ofneighbors found in the cache. If no result can be found in the shadercache, the fragment shader program is executed also for the approximatedview.

To relate the exact and approximate views, a mapping algorithm isprovided, using texture coordinates. The texture coordinates may e.g. beperspective-correct barycentric coordinates. The algorithm maps aposition of a primitive in an approximated view to a position in theassociated exact view.

The shader output cache 62 is provided where recent fragment informationfrom one or more exact views is stored and can be accessed forassociated approximated views.

According to some embodiments, a method of rendering a three-dimensionalimage on a display comprising performing pixel traversal of a primitiveafter projection of the primitive is provided. The method comprises thestep of approximating and reusing fragment shader program output fromadjacent views.

In the embodiment of FIG. 5, the approximation unit 61 is configured toprocess fragments differently depending on if the pair, to which thatfragment belongs, is associated with an “exact view” or an “approximatedview”. The exact views may consist of one or more selected views fromthe plurality of views, and are exact in the sense that rendering isdone to them by executing the fragment shader program using the FPU 55.Hence, no approximation is done for exact views.

The approximated views are selected as the remaining views of theplurality of views. Each approximated view is associated with an exactview. For each approximated view, the associated exact view is typicallythe exact view that is “closest”, in terms of view parameters, to theapproximated view.

According to one embodiment of the invention, the exact view renders aprimitive by executing the fragment shader program, and the output fromthis execution is called “shader output”. If possible, approximatedviews may reuse the shader output from the exact views, and weighttogether one or several shader outputs in order to generate approximatefragment outputs for approximated views.

If the currently processed fragment belongs to an exact view, thefragment shader program is executed using the FPU 55. The outputs of thefragment shader program, e.g., color, depth, stencil, etc., may bewritten to the shader output cache memory 62 before being passed furtherdown the graphics pipeline. The shader output cache 62 may be dedicatedon-chip memory, a set of flip-flops, or stored in off-chip memory, orusing any other storage method.

If the currently processed fragment belongs to an approximated view, theinformation gathered while processing the associated exact view may beused to approximate the fragment shader program output of theapproximated view. The fragment coordinates are projected onto theviewing plane of the corresponding exact view. This can be done byinterpolating the positions of the vertices of the triangle in thecorresponding exact view (denoted p, q, and r), using theperspective-correct interpolation parameters for the fragment in theapproximated view (denoted tu and tv). The interpolation may be done onthe form:c=(1−tu−tv)·p+tu·q+tv·r.

It is to be appreciated that these computations can be done in manyother different ways, and that the approximation disclosed herein workswith them as well.

The interpolated position, c, may then be projected to compute a screenspace position for the current fragment in the context of the exactview. This projected position may be used to query the shader outputcache memory 62 for the shader output of fragments in the neighborhoodof the projected position. The shader output of a fragment in theapproximated view may be computed using a filter kernel based therelationship of a fragment in the approximated view, and the exact view.Furthermore, it may be computed using linear interpolation between thetwo closest neighbors in the shader output cache 62, or simply set tothe nearest neighbor if no two fragments can be found in the extents ofthe neighborhood. This may for instance occur when a fragment lie closeto the edge of a triangle.

According to an embodiment, two positions, whose arithmetic average isthe position of a fragment of the approximated view, are projected intothe exact view. If fragments of the exact view in neighborhoods of theprojected positions are stored in the shader output cache 62, thefragment of the approximated view is generated based on said fragmentsin said neighborhoods. Otherwise, the fragment of the approximated viewis generated by executing the fragment shader program.

The shader output cache 62 may be cleared between the renderings ofprimitives, to avoid accidental use of data from other primitives whileapproximating the fragment shader program output for a fragment. Theshader output cache 62 may use a cyclic replacement strategy, when thetraversal order of the rasterizer 53 is incremental, i.e., one traversesas much as possible to neighboring tiles. In this case, the cyclicreplacement strategy will efficiently work as a least recently used(LRU) replacement strategy. Other replacement strategies may be combinedwith our invention as well.

The shader output 62 cache may be structured as individual fragments, oras group of fragments. The shader output cache 62 may be an individualcache memory, or extend already existing cache memory such as a colorbuffer cache. Extending the color buffer cache has the drawback of notbeing able to use approximation when blending is enabled.

The efficiency measure (M_(i)) of a fragment, or a pair, may bepenalized for approximated views by effectively computing the efficiencymeasure of a fragment, or a pair, further down in the traversal order.This will effectively delay the approximated views, allowing the exactviews to fill the shader output cache memory 62 with relevant data. Theadvantage of this is that the chance that an approximated view canapproximate the fragment outputs is increased.

It should also be appreciated that the exact view(s) may change from onerendering primitive to the next. This may be advantageous. For example,better performance has been achieved in simulations when the exact viewis chosen as the view where the projection area of the primitive is thelargest.

The approximation disclosed herein may also be used for accumulativecolor rendering. For this, the exact view(s) and the approximatedview(s) have separate depth buffers as usual, but they all share asingle color buffer. When rendering, the output color is blended intothe color buffer. This can be used to render a single-view image withdepth of field, for example. Other possible usages are motion blur andanti-aliasing.

The invention may be embedded in a computer program product, whichenables implementation of the method and functions described herein. Theinvention may be carried out when the computer program product is loadedand run in a system having computer capabilities. Computer program,software program, program product, or software, in the present contextmean any expression, in any programming language, code or notation, of aset of instructions intended to cause a system having a processingcapability to perform a particular function directly or after conversionto another language, code or notation.

Finally, as is illustrated in FIGS. 2 and 5, the RSU 22, 52, therasterizer 23, 53, the Z-cull 24, 54, the FPU 25, 55, the TCM 26, 56,and the ZC&B 28, 58 may be duplicated. Although this is not necessaryfor carrying out the invention, this may in some cases improve theperformance of the CGP 20, 50 even further. Note, however, that it isnot necessary to duplicate the PVS 21, 51 or the EXM 27, 57.Nevertheless, in some embodiments the PVS 21, 51 may require minormodification to handle a plurality of views.

It is an advantage with embodiments of the invention that they may allowfor a reduction of the required utilization of memory-bandwidth of acomputer graphics processor. For embodiments utilizing the abovedescribed approximated and exact views, a further advantage is that thenumber of times the FPU 55 executes the fragment shader program isdecreased substantially. This may be advantageous since the execution ofthe fragment shader program may limit the obtained performance.

It has been shown in simulations for a particular 3D scene, renderedfrom four different views, that a conventional computer graphicsprocessor generally utilizes up to 220% more bandwidth to the texturecache memory device compared to embodiments of the present invention.Consequently, embodiments of the invention may allow for an improvementof the performance of computer graphics processors.

In simulations of a CGP utilizing approximated and exact views, it hasbeen shown that the obtained image quality is high and that the numberof approximated fragments is high as well. The image quality can bemeasured using PSNR (peak signal to noise ratio), and it has been around43 dB (decibel), which is considered to be high quality even instill-image compression. The number of approximated fragments in theapproximated views has often been as high as 95%, which means that only5% of the fragments execute the full fragment shader program.

It is thus a further advantage that a computer graphics processor andmethod according to embodiments of the invention may provide 3D imageson a display screen with good image quality without the need ofexcessive use of memory-bandwidth. In terms of implementation, onlymodest changes to a conventional GPU may be needed. Thus, the additionalmanufacturing costs of a computer graphics processor enabling good imagequality at improved performance is relatively low. Embodiments of theinvention may preferably be implemented in devices with limited size,such as mobile telephones, portable computers, etc. Moreover, whenimplemented in e.g. a mobile telephone or other battery powered device,embodiments of the invention may provide for the avoidance of drainingthe battery quickly. However, embodiments of the invention are notlimited to above-mentioned devices. Other devices where embodiments ofthe invention may be implemented include e.g. desktop PCs, laptops, gameconsoles, 3D TVs, glasses with built-in-displays, but is not limited tothese applications.

The present invention has been described above with reference tospecific embodiments. However, other embodiments than the abovedescribed are possible within the scope of the invention. Differentmethod steps than those described above, performing the method byhardware or software or a combination of hardware and software, may beprovided within the scope of the invention. The different features andsteps of the invention may be combined in other combinations than thosedescribed. The scope of the invention is only limited by the appendedpatent claims.

The invention claimed is:
 1. A computer graphics processor comprising: arasterizer to perform pixel traversal of a primitive after projection ofthe primitive to perform the pixel traversal of a first primitive for aplurality of views prior to performing pixel traversal of a nextprimitive for one or more views; wherein the computer graphics processorto for at least a first view, generate fragments of the at least firstview by executing a fragment shader program; and for at least a secondview, generate fragments of the at least second view based on thegenerated fragments of the at least first view.
 2. The computer graphicsprocessor of claim 1, wherein the rasterizer to perform the pixeltraversal of the first primitive for all views of the plurality of viewsprior to performing pixel traversal of the next primitive for all viewsof the plurality of views.
 3. The computer graphics processor of claim2, wherein the rasterizer is configured to perform pixel traversal for apair of the first primitive, the pair comprising a group of pixels and aparticular view, and then continue with another pair for the firstprimitive, and so on, until the first primitive has been fullytraversed, prior to performing pixel traversal of the next primitive inthe same manner as the first primitive.
 4. The computer graphicsprocessor of claim 3, wherein the rasterizer is operatively connected toa selector adapted to determine an order in which the pairs are to beprocessed by the rasterizer during the pixel traversal of theprimitives.
 5. The computer graphics processor of claim 4, wherein theselector is configured to determine said order based on an efficiencymeasure for each view of the plurality of views and wherein the selectoris configured to determine said efficiency measure based on$M_{i} = \left\lbrack \begin{matrix}{du} & {\left. {dv} \right\rbrack,\begin{bmatrix}{tui} \\{tvi}\end{bmatrix}}\end{matrix} \right.$ which corresponds to projecting the texturecoordinate (tui,tvi) of a representative point of a group of pixels ontothe texture traversal direction (du,dv) in texture space, and M_(i) isthe efficiency measure for a view i, and where said group of pixels isnext subject to traversal for view i, and the view that is selected fortraversal next is the view k, where M_(k) is the lowest value of allM_(i) .
 6. The computer graphics processor according to claim 1, whereinthe computer graphics processor comprises a memory and is adapted totemporarily store the generated fragments of the first view in thememory; and for the second view, generate a fragment of the second viewby projecting a position of the fragment of the second view into thefirst view; if fragments of the first view in a neighborhood of theprojected position of the fragment of the second view are stored in thememory, generating the fragment of the second view based on saidfragments in said neighborhood; or otherwise generating the fragment ofthe second view by executing the fragment shader program for thefragment of the second view.
 7. The computer graphics processoraccording to claim 6, wherein the computer graphics processor is adaptedto generate texture coordinates for the fragment of the second view anduse these texture coordinates to project the position of the fragment ofthe second view into the first view.
 8. The computer graphics processoraccording to claim 6, wherein the computer graphics processor is adaptedto generate the fragment of the second view based on said fragments insaid neighborhood as a weighted average of said fragments in saidneighborhood.
 9. The computer graphics processor according to claim 6,wherein the computer graphics processor is adapted to if at least twofragments of the first view in said neighborhood is stored in thememory, generate the fragment of the second view by performing linearinterpolation on the two of said at least two fragments that are closestto said projected position; or if exactly one fragment of the first viewin said neighborhood is stored in the memory, generate the fragment ofthe second view identical to said exactly one fragment.
 10. The computergraphics processor according to claim 1, wherein the computer graphicsprocessor comprises a memory and is adapted to temporarily store thegenerated fragments of the first view in the memory; and for the secondview, generate a fragment of the second view by projecting twopositions, whose arithmetic average is the position of the fragment ofthe second view, into the first view; if fragments of the first view inneighborhoods of the projected positions are stored in the memory,generating the fragment of the second view based on said fragments insaid neighborhoods; or otherwise generating the fragment of the secondview by executing the fragment shader program for the fragment of thesecond view.
 11. The computer graphics processor according to claim 1,wherein the computer graphics processor is adapted to weight fragmentsof a view into a common color buffer.
 12. A method of rendering athree-dimensional image on a display, comprising: performing on agraphics processor pixel traversal of a primitive after projection ofthe primitive; performing the pixel traversal on the graphics processorof a first primitive for a plurality of views prior to performing pixeltraversal of a next primitive for one or more views; generatingfragments of at least a first view by executing a fragment shaderprogram; and generating fragments of at least a second view based on thegenerated fragments of the at least first view.
 13. The method of claim12, wherein the step of performing comprises performing the pixeltraversal of the first primitive for all views of the plurality of viewsprior to performing pixel traversal of a next primitive for all views ofthe plurality of views.
 14. The method of claim 12, wherein the step ofperforming comprises performing pixel traversal for a pair of the firstprimitive, the pair comprising a group of pixels and a particular view,and continuing with another pair for the first primitive, and so on,until the first primitive has been fully traversed, prior to performingpixel traversal of the next primitive in the same manner as the firstprimitive.
 15. The method of claim 14, further comprising: determiningan order in which the pairs are to be processed during the pixeltraversal of the primitives.
 16. The method of claim 15, wherein thestep of determining comprises: determining said order based on anefficiency measure for each view of the plurality of views, anddetermining said efficiency measure based on$M_{i} = \left\lbrack \begin{matrix}{du} & {\left. {dv} \right\rbrack,\begin{bmatrix}{tui} \\{tvi}\end{bmatrix}}\end{matrix} \right.$  which corresponds to projecting the texturecoordinate (tui,tvi) of a representative point of a group of pixels ontothe texture traversal direction (du,dv) in texture space, and M_(i) isthe efficiency measure for a view i, and where said group of pixels isnext subject to traversal for view i, and the view that is selected fortraversal next is the view k, where M_(k) is the lowest value.
 17. Acomputer graphics processor comprising: a rasterizer to perform pixeltraversal of a primitive after projection of the primitive, to performthe pixel traversal of a first primitive for a plurality of views priorto performing pixel traversal of a next primitive for one or more views;and wherein the computer graphics processor is adapted to weightfragments of a view into a common color buffer.
 18. The computergraphics processor of claim 17, wherein the rasterizer to perform thepixel traversal of the first primitive for all views of the plurality ofviews prior to performing pixel traversal of the next primitive for allviews of the plurality of views.
 19. The computer graphics processor ofclaim 18, wherein the rasterizer is configured to perform pixeltraversal for a pair of the first primitive, the pair comprising a groupof pixels and a particular view, and then continue with another pair forthe first primitive, and so on, until the first primitive has been fullytraversed, prior to performing pixel traversal of the next primitive inthe same manner as the first primitive.
 20. The computer graphicsprocessor of claim 19, wherein the rasterizer is operatively connectedto a selector adapted to determine an order in which the pairs are to beprocessed by the rasterizer during the pixel traversal of theprimitives.
 21. The computer graphics processor of claim 20, wherein theselector is configured to determine said order based on an efficiencymeasure for each view of the plurality of views and wherein the selectoris configured to determine said efficiency measure based on${M_{i} = \left\lbrack {{du}\mspace{14mu}{dv}} \right\rbrack},\begin{bmatrix}{tui} \\{tvi}\end{bmatrix}$ which corresponds to projecting the texture coordinate(tui,tvi) of a representative point of a group of pixels onto thetexture traversal direction (du,dv) in texture space, and M_(i) is theefficiency measure for a view i, and where said group of pixels is nextsubject to traversal for view i, and the view that is selected fortraversal next is the view k, where M_(k) is the lowest value of allM_(i).
 22. The computer graphics processor according to claim 17,wherein the computer graphics processor to for at least a first view,generate fragments of the at least first view by executing a fragmentshader program, and for at least a second view, generate fragments ofthe at least second view based on the generated fragments of the atleast first view, wherein the computer the computer graphics processorcomprises a memory and is adapted to temporarily store the generatedfragments of the first view in the memory; and for the second view,generate a fragment of the second view by projecting a position of thefragment of the second view into the first view; if fragments of thefirst view in a neighborhood of the projected position of the fragmentof the second view are stored in the memory, generating the fragment ofthe second view based on said fragments in said neighborhood; orotherwise generating the fragment of the second view by executing thefragment shader program for the fragment of the second view.
 23. Thecomputer graphics processor of claim 22, wherein the computer graphicsprocessor is adapted to generate texture coordinates for the fragment ofthe second view and use these texture coordinates to project theposition of the fragment of the second view into the first view.
 24. Thecomputer graphics processor of claim 22, wherein the computer graphicsprocessor is adapted to generate the fragment of the second view basedon said fragments in said neighborhood as a weighted average of saidfragments in said neighborhood.
 25. The computer graphics processor ofclaim 22, wherein the computer graphics processor is adapted to if atleast two fragments of the first view in said neighborhood is stored inthe memory, generate the fragment of the second view by performinglinear interpolation on the two of said at least two fragments that areclosest to said projected position; or if exactly one fragment of thefirst view in said neighborhood is stored in the memory, generate thefragment of the second view identical to said exactly one fragment. 26.The computer graphics processor of claim 22, wherein the computergraphics processor to for at least a first view, generate fragments ofthe at least first view by executing a fragment shader program, and forat least a second view, generate fragments of the at least second viewbased on the generated fragments of the at least first view, wherein thecomputer graphics processor comprises a memory and is adapted totemporarily store the generated fragments of the first view in thememory; and for the second view, generate a fragment of the second viewby projecting two positions, whose arithmetic average is the position ofthe fragment of the second view, into the first view; if fragments ofthe first view in neighborhoods of the projected positions are stored inthe memory, generating the fragment of the second view based on saidfragments in said neighborhoods; or otherwise generating the fragment ofthe second view by executing the fragment shader program for thefragment of the second view.